The Shatapatha Brahmana

The Shatapatha Brahmana is a prose text describing Vedic rituals, history and mythology associated with the Śukla Yajurveda.

Brahmagupta's Formula

628 BC

Brahmagupta's formula: The area, A, of a cyclic quadrilateral with sides of lengths a, b, c, d, respectively, is given by

Pythagorean Triples

600 BC

the other Vedic “Sulba Sutras” (“rule of chords” in Sanskrit) use Pythagorean triples, contain of a number of geometrical proofs, and approximate π at 3.16

Pappus Of Alexandria

340 BC

Pappus of Alexandria states his hexagon theorem and his centroid theorem

Hipparchus develops the bases of trigonometry.

140 BC

The Nine Chapters on the Mathematical Art

100 BC

The Nine Chapters on The Mathematical Art lays out an approach to mathematics that centers on finding the most general methods of solving problems

Greece

Thales of Miletus

Approx. 624 BC - Approx. 546 BC

Created and proved Thales Theorem DE/BC=AE/AC=AD/AB

Pythagoras

Approx. 570 BC - Approx. 495 BC

Pythagorean theorem is named after him although its not been proven that he ever even existed
A2+B2=C2

Zeno's Paradoxes

Approx. 455 BC

A set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea

Greeks use numerals

Approx. 450 BC

First recorded incident of written numerals in Greece

Plato

427 BC - 347 BC

a philosopher that is highly esteemed by the Greeks. There is a story that he had inscribed above the entrance to his famous school, "Let none ignorant of geometry enter here." However, the story is considered to be untrue.
He was NOT a mathematician however his views helped shape many concepts

After Achimedes

410 BC

After Archimedes died hellenistic geometry started to decline in popularity

Plato's Polyhedra

Approx. 387 BC

Plato founds the Academy in Athens. He identifies five polyhedra now known as Platonic bodies.

Eudoxus Rational and Irrational Comparison

Approx. 360 BC

Eudoxus makes a definition allowing the possibility of using irrational lengths and comparing them with rational lengths by using cross multiplication.

Euclid

Approx. 325 BC - Approx. 265 BC

Euclid is considered to be one of the three greatest mathematicians of all time. He discovered Euclidean geometry which use his axioms and theorems as they relate to plane and solid figures.

The Elements

Approx. 300 BC

Euclid writes The Elements, a book discussing Euclidean geometry. The Elements is a collection of 13 books of definitions, postulates, and axioms. It became the 3rd most popular book in the world, after the Koran and the Bible.

Archimedes

Approx. 287 BC - Approx. 212 BC

Archimedes is regarded as the greatest Greek mathematician. He invented 3 simple machines, the pulley, screw, and lever. The Archimedes screw, a device used for raising water, is still in use today. He also analyzed the area of a circle and discovered how to calculate volumes and surface areas of spheres and cylinders.

Volume of a cylinder

Approx. 250 BC

Archimedes discovers the formula for how to calculate the volume of a cylinder.

The Earth's Circumference

235 BC

Eratosthenes estimates the circumference of the Earth, only missing by about 15%.

Medieval Geometry

Area of an Encircled Quadrilateral

Approx. 628 AD

Brahmagupta created a formula for finding the area of a quadrilateral, with sides a,b,c,d, enclosed by a circle: A = The Sq. Root of (s-a)(s-b)(s-c)(s-d). S is the semi-perimeter, is found by the formula s=(a+b+c+d)/2

Synthesis of Algebra and Geometry

Approx. 853 AD

Modern Age Geometry

Renee Descartes

1596 - 1650

Descartes synthesized algebra and geometry by placing points on a coordinate plane.

Paddhati

1600

Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series

Isaac Newton

25 December 1643 - 20 March 1727

Widely known as a the man who helped revolutionize the concept of gravity Newton made several contributions to mathematics and geometry as well as science including being credited as one of the fathers of calculus.

Gottfried Wilhelm Leibniz

July 1 1646 - November 14 1716

Leibniz was a German mathematician who is credited as also being a father of modern calculus

Calculus

1684

Even though there is much controversy surrounding it its widely believed that Sir Isaac Newton and Gottfried Wilhelm Leibniz both discovered/created calculus in the mid 17th century

Carl Friedrich Gauss

1777 - 1855

Gauss developed the Gauss method for adding large amounts of consecutive numbers when he was six. However, his most important creation is that of non-Euclidean geometry. Non-Euclidean geometry is geometry not based on the postulates of Euclid. This includes times when the parallel postulate isn't true. Parallel Postulate - Through a given point not on a line, there is one and only one line parallel to it.

Kepler-Poinsot polyhedra.

1806

Louis Poinsot discovers the two remaining Kepler-Poinsot polyhedra.

George Friedrich Bernhard Riemann

1826 AD - 1866 AD

Riemann was one of the foremost geometers in the development of Non-Euclidean Geometry. He also was a lecturer at the University of Gottingen

Arthur Cayley

1854 AD

1854 – Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space.

Ferdinand von Lindemann

1882

Ferdinand von Lindemann proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,

Three Cottage Problem Disproved

1930 AD

Casimir Kuratowski shows that the three-cottage problem has no solution
The problem is as follows:
"Suppose there are three cottages on a plane (or sphere) and each needs to be connected to the gas, water, and electricity companies. Without using a third dimension or sending any of the connections through another company or cottage, is there a way to make all nine connections without any of the lines crossing each other?"